Single-digit-micrometer-resolution continuous liquid interface production

To date, a compromise between resolution and print speed has rendered most high-resolution additive manufacturing technologies unscalable with limited applications. By combining a reduction lens optics system for single-digit-micrometer resolution, an in-line camera system for contrast-based sharpness optimization, and continuous liquid interface production (CLIP) technology for high scalability, we introduce a single-digit-micrometer-resolution CLIP-based 3D printer that can create millimeter-scale 3D prints with single-digit-micrometer-resolution features in just a few minutes. A simulation model is developed in parallel to probe the fundamental governing principles in optics, chemical kinetics, and mass transport in the 3D printing process. A print strategy with tunable parameters informed by the simulation model is adopted to achieve both the optimal resolution and the maximum print speed. Together, the high-resolution 3D CLIP printer has opened the door to various applications including, but not limited to, biomedical, MEMS, and microelectronics.


Image analysis scheme for extracting 2D printed feature from SEM images
An image analysis scheme is applied to extract the line width from the SEM images. Shown here is a sample line edge profile extracted from a 15µm width line design obtained from SEM. The SEM images are first imported into ImageJ and a single line or hole edge profile is extracted (Fig. S2). The edge profile is then subjected to a simple algorithm through peak and valley extraction. The critical dimension (CD) extracted from the SEM is based on the 50% intensity threshold method [66], where the line width reported is based on the x-coordinates extracted at the 50% intensity threshold at the outer edge.

Model parameters used in the transport and kinetics model
The final solution of the coupled partial differential equations (PDEs) for both the un-reacted monomer concentration and the oxygen concentration is obtained through MATLAB PDE solver and the parameters used can be found in Figures. 5(a-d). While some parameters are directly obtained through references, there are also values that were estimated or directly measured. We provide a brief discussion of the estimated parameters.
The initial exposure time for resin to cure onto the build platform is roughly around 3s experimentally, depending on the design. Therefore, this gives us a rough estimation of H which should be around 10µm, given that 3s is sufficient for print part to adhere onto the build platform for continuous print to proceed.
Note that while we don't have a direct measurement of the exact light intensity from the 3.5µm or 1.5µm lens, however we did a rough estimation from the intensity that was configured for the 30 µm lens. The intensity 0 is obtained using the approximation of the known maximum intensity of our light engine for a 30µm printer, which is around 40mW/cm 2 . The current value is assumed to linearly scaled by the related Lightcrafter 0-255 control. Nonlinearities in the LED itself as well as temperature fluctuations in the final light intensity have not been considered. To obtain the rough estimation of the light intensity, we took account for the single pixel projected area reduction (30µm: 30; 3.5µm: 3.75; 1.5µm: 1.5) along with f # differences (30µm: 1.3; 3.5µm: 12; 1.5µm: 16). With the listed details, we estimated the initial exposure at UV intensity 1 is 1.1W/m 2 for 3.5µm lens and 4 for 1.5µm lens.
The [ ] concentration is obtained from known photo-initiator concentration 2.5 wt% that is used in our system.
The oxygen concentration at the surface of the window is estimated to be 3 times the concentration of a PDMS surface, due to the fact that a Teflon AF 2400 has 3 times higher permeability to oxygen than PDMS [55]. Further experimental validation of the modeling parameters is crucial for a more accurate prediction. We also note that several key elements of oxygen transport are currently ignored, including the solubility of oxygen in the TMPTA resin as well as the permeability of oxygen through the Teflon AF 2400 window. We use model parameters obtained from known references as a rational framework to understand the CLIP printing process and dead-zone formation.

Derivation of lubrication theory applied to CLIP technology -Newtonian fluid
From the CLIP schematic in (Fig. 4), the derivation of the lubrication theory after applying the appropriate scaling ~ℎ ; �~; � , �~ ; � = ; � = ; ̃= ℎ and assuming ≪ 1, we obtained the simplified governing equations for Newtonian fluid as follows: Continuity equation: Where ∇ is the gradient operator in the � − � plane, The corresponding boundary conditions for the velocity are and (ℎ) is used to describe the velocity of the top plate. From (Eq. (3)), pressure is thus only a function of (0) ( , ).
We can then integrate (Eq. (2)) and applied boundary conditions To solve for , and determine p we integrate (Eq. (4)) from 0 to h: Applying boundary conditions, we obtain From (Eq. (4)), we know Substituting into (Eq. (6)), we obtain Assuming gap thickness ℎ is a constant, we obtain (ℎ) = ∇ 2 � ℎ 3 12 � (9) We can further express as Therefore, If we assume at surface of plate, both velocity and height are maximum and normalized to 1, we can thus set (ℎ) = 1 and ℎ = 1, we then obtain the velocity profile in both x and z direction in the dead-zone regime as follows: We can solve for the pressure field within the dead-zone regime if we first assume the part footprint is instantaneously a cylinder and L is the radius of the cylinder. Moreover, we assume = 0,̃= 1. Integrating (Eq. (9)) then gives: We can then integrate the pressure within the circular build area to obtain the Stefan force:

Derivation of lubrication theory applied to CLIP technology -non-Newtonian fluid
For a non-Newtonian power-law fluid we assume. Note that for Newtonian fluid, n = 0.

Resin stress relaxation time and print radius
The transient stress relaxation time required for resin (TMPTA + 0.3wt% BLS1326 + 2.5wt% TPO) with print diameter ranging from 0.4cm to 2.2cm is plotted in Figure. S5 (a). The longest relaxation time is extracted by replotting Figure. S5 (a) in semi-log plot to extract the average longest relaxation time within the transient stress-relaxation process. It is found that the stress-relaxation time increases with increased diameter. Finally, we are aware of the effect of resin shrinkage during curing has a potential impact on the stress-relaxation. However, from Figure. S4 (a) within the 100ms during exposure time, there's no observable relaxation occurring. Ongoing efforts include using Optical Coherence Tomography (OCT) to better elucidate the effect.

Resin re-flow and print defects under insufficient interlayer time
Based on our prediction on the required time for resin to reflow for the 8.9mm by 5.6mm square area for a resin (TMPTA + 0.3wt% BLS1326 + 2.5wt% TPO) with viscosity approximately 0.2PaS at shear rate of 0.1 (1/s), we have conducted a characterization of the defect versus the interlayer time. The measured interlayer time showed that the defect is gone after approximately at > 200ms (Fig. S4).